Which of the following options would be the equation of a line perpendicular to the line y=−3x+5

Question

?(1 point)
Responses

y=−13x+9
y equals negative Start Fraction 1 over 3 End Fraction x plus 9

y=3x+9
y equals 3 x plus 9

y=13x+9
y equals Start Fraction 1 over 3 End Fraction x plus 9

y=−3x+9

Answer 1

To find a line that is perpendicular to the line given by the equation \( y = -3x + 5 \), we need to determine the slope of the given line and then find the negative reciprocal of that slope.

1. The slope of the given line \( y = -3x + 5 \) is \(-3\).
2. The negative reciprocal of \(-3\) is \(\frac{1}{3}\).

Now, we look for a line whose slope is \(\frac{1}{3}\).

Among the options provided, we can identify the equation that has this slope:

• \( y = \frac{1}{3}x + 9 \) (This has the correct slope of \(\frac{1}{3}\))

The other options have different slopes, so the line perpendicular to \( y = -3x + 5 \) is:

y = \(\frac{1}{3}x + 9\) (y equals Start Fraction 1 over 3 End Fraction x plus 9).